Full Idea
It is far from obvious that knowing what 'just as many' means requires knowing what a one-one correspondence is. The notion of a one-one correspondence is very sophisticated, and it is far from clear that five-year-olds have any grasp of it.
Gist of Idea
Understanding 'just as many' needn't involve grasping one-one correspondence
Source
Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 4)
Book Reference
-: 'Notre Dame Journal of Formal Logic' [-], p.198
A Reaction
The point is that children decide 'just as many' by counting each group and arriving at the same numeral, not by matching up. He cites psychological research by Gelman and Galistel.